Simple model of kinetic roughening of quasicrystalline surfaces

A simple relaxational model of the dynamics of the surface of a growing quasicrystal is studied. As in a crystal, growth proceeds through the nucleation of steps on the surface. Unlike the crystal, the heights hₛ of these steps diverge like ({Δ}{μ})^-1/3 as the driving chemical-potential difference {Δ}{μ} between quasicrystal and fluid goes to zero. The exponent 1/3 is universal for all quasicrystals with structures derived from quadratic irrationals. This large step size leads to unusually low growth velocities Vg; i.e., Vg{∝}exp{-1/3[{Δ}uc(T)/{Δ}{μ}]4/3}. The quantity {Δ}μc(T), which defines a rounded kinetic roughening transition, is nonuniversal. For ``perfect-tiling models'' of quasicrystal growth, I find {Δ}μc(T){∝}T^-3/2, which fits recent numerical simulations, while for models which allow bulk phason Debye-Waller disorder, ln(1/{Δ}μc){∝}T3/2. The growing interface is algebraically rough at all temperatures.